Distance Metric Learning

The foundational training paradigm that organizes embedding spaces using anchor-positive-negative triplets. The loss function pulls the anchor and positive (same class) together while pushing the negative (different class) beyond a margin parameter.

• Minimizes intra-class distance while maximizing inter-class separation
• Hard negative mining selects the most confusable dissimilar samples for efficient training
• Critical for open set recognition where tight class clusters define rejection boundaries

Advanced loss functions including ArcFace, CosFace, and SphereFace that enforce discriminative constraints directly on the hyperspherical angle between feature vectors rather than Euclidean distance.

• Additive angular margin creates more separable class boundaries
• Normalizes both weights and features to lie on a unit hypersphere
• Produces embeddings where cosine similarity reliably indicates class membership for open set thresholding

A statistically-grounded metric that measures distance accounting for the covariance structure of each class distribution, unlike Euclidean distance which assumes isotropic variance.

• Computes how many standard deviations a sample lies from the class mean
• Naturally captures elliptical class shapes common in real-world feature distributions
• Provides calibrated confidence scores for out-of-distribution detection by modeling per-class Gaussian densities

A framework where each class is represented by a single prototypical vector—typically the mean embedding of support examples—and query samples are classified by nearest-prototype distance.

• Inherently supports open set rejection: samples far from all prototypes are unknown
• Enables few-shot enrollment by computing prototypes from minimal examples
• Used in Prototypical Networks for rapid device authentication with limited training data

Self-supervised approaches including SimCLR and SupCon that learn distance metrics without explicit class labels by maximizing agreement between differently augmented views of the same sample.

• Pulls positive pairs together while pushing all other samples apart in the batch
• Learns invariances to nuisance transformations like noise and channel distortion
• Pre-trained contrastive embeddings transfer effectively to open set emitter recognition tasks

A one-class distance metric approach that trains a neural network to map all normal training data into a minimal-volume hypersphere centered at a learned point.

• Anomalies and unknown classes fall outside the hypersphere boundary
• Eliminates the need for negative samples during training
• Effective for open set rejection when only known-class data is available for enrollment

A parametric distance metric that measures the distance between a point and a distribution, accounting for feature covariance. Unlike Euclidean distance, it scales axes by the inverse of the covariance matrix, effectively down-weighting noisy or correlated features. In open set recognition, Mahalanobis distance is used to compute the probability that a new emitter belongs to a known class by measuring how many standard deviations away it lies from the class mean. This provides a statistically principled rejection threshold that adapts to the natural variance of each transmitter's fingerprint.

A family of loss functions—including ArcFace, CosFace, and SphereFace—that enforce discriminative constraints on the angular space of feature embeddings. By adding an additive angular margin penalty between class prototypes and sample embeddings, these losses maximize inter-class separation while compressing intra-class variance. For RF fingerprinting, angular margin losses produce highly compact clusters for known emitters, leaving large angular gaps where unknown devices naturally fall, enabling robust open set rejection without explicit outlier training data.

A self-supervised representation learning framework that trains encoders by pulling positive pairs (augmentations of the same sample or same-class emitters) together and pushing negative pairs (different emitters or noise) apart in embedding space. Frameworks like SimCLR and SupCon use a temperature-scaled cross-entropy objective over similarity scores. In open set emitter recognition, contrastive pretraining on unlabeled RF captures creates a structured metric space where distance directly corresponds to transmitter identity, even before any explicit class labels are introduced.

A few-shot learning architecture that represents each class by a single prototype vector—the mean embedding of its support examples. Classification is performed by computing distances (typically Euclidean) from a query sample to all class prototypes and applying SoftMax over negative distances. For device enrollment in RF systems, prototypical networks enable rapid onboarding of new transmitters using only 1-5 example transmissions, with unknown emitters naturally identified when their distance to all known prototypes exceeds a calibrated threshold.

A metric learning objective that operates on triplets of samples: an anchor, a positive (same class), and a negative (different class). The loss penalizes embeddings where the anchor-positive distance exceeds the anchor-negative distance by less than a margin parameter. Triplet loss directly optimizes for relative distance relationships rather than absolute positions. In RF fingerprinting, hard triplet mining—selecting the most confusable negative emitters—produces embedding spaces where even subtle hardware impairment differences become geometrically separable.

Deep Support Vector Data Description is a one-class classification method that trains a neural network to map normal (known emitter) data into a minimal-volume hypersphere centered at a learned point. Anomalies and unknown emitters are identified when their embeddings fall outside this compact boundary. Unlike discriminative approaches, Deep SVDD requires only known-class data during training, making it ideal for open set RF scenarios where comprehensive samples of all possible unknown devices cannot be collected in advance.